By substituting arbitrary values for the variable and deciding the roots of quadratic equation is a time consuming process. Let us learn to use factorisation method to find the roots of the given quadratic equation.
x2 - 4 x - 5 = (x - 5) (x + 1)
(x - 5) and (x + 1) are two linear factors of quadratic polynomial x2 - 4 x - 5.
So the quadratic equation obtained from x2 - 4 x - 5 can be written as (x - 5) (x + 1) = 0
If product of two numbers is zero then at least one of them is zero.
x - 5 = 0 or x + 1 = 0
∴x = 5 or x = -1
∴5 and the -1 are the roots of the given quadratic equation.
While solving the equation first we obtained the linear factors. So we call this method as ’factorization method’ of solving quadratic equation.
Ex.(1) m2 - 14 m + 13 = 0
∴m2 - 13 m - 1m + 13 = 0
∴m (m - 13) -1 (m - 13) = 0
∴(m - 13) (m - 1) = 0
∴m - 13 = 0 or m - 1 = 0
∴m = 13 or m = 1
∴13 and 1 are the roots of the given quadratic equation.
The distance between Akola and Bhusawal is 168 km. An express train takes 1 hour less than a passenger train to cover the distance. Find the average speed of each train if the average speed of the express train is more by 14 km/hr than the speed of the passenger train.